Question

solving for an unknown segment length
what is the length of segment lm?
units

Explanation:

Step1: Set up equation

Since \(NK = NM\) (given the marks indicating congruence), we have \(14x - 3=25\).

Step2: Solve for \(x\)

Add \(3\) to both sides: \(14x=25 + 3\), so \(14x=28\). Then divide both sides by \(14\): \(x=\frac{28}{14}=2\).

Step3: Find \(KL\)

Substitute \(x = 2\) into \(9x + 5\). So \(KL=9\times2+5=18 + 5=23\).

Step4: Use congruence (HL - Hypotenuse - Leg for right triangles)

Since \(\triangle NLK\cong\triangle NLM\) (right - angled triangles with \(NK = NM\) and \(NL\) common), \(LM=KL\).

Answer:

\(23\)